Читать книгу Spatial Multidimensional Cooperative Transmission Theories And Key Technologies - Lin Bai - Страница 55

In order to reduce the complexity of detection, we can also consider using the linear filtering method to complete the detection process. In the linear MIMO signal detection, each transmitted signal can be detected separately after the received signal y is filtered by a linear filter. Therefore, the function of a linear filter is to separate the interference signals.

First, we consider zero forcing (ZF) detection. The ZF detection linear filter is defined as

And the corresponding ZF signal is estimated as

With and , the hard decision of the transmitted signal vector s can be made by the symbol-level estimation.

It should be noted that since the noise term, namely the effect of (H^HH)⁻¹H^Hn in Eq. (2.148), will be amplified, the equivalent noise will be amplified when the channel matrix H is nearly singular. Therefore, the performance of the ZF detection cannot be well guaranteed. In order to reduce the influence caused by the equivalent noise being amplified in the ZF detection, the MMSE detection utilizes the statistical property of the noise to improve the ZF detection method. The calculation of the MMSE filter matrix is based on the minimum mean square error criterion.

where E_s represents the signal energy. The corresponding estimate of the transmitted signal vector can be expressed as

Therefore, the MMSE hard decision of the signal vector s can be obtained.